A semiconductor device, liquid crystal display element, image capturing device (CCD: Charge Coupled Device etc.), thin film magnetic head, and various other types of devices are mostly produced by using an exposure apparatus to transfer by exposure multiple layers of patterns overlaid on a substrate. For this reason, when transferring by exposure the second layer and later layers of patterns on a substrate, the shot areas already formed with patterns on the substrate and the pattern images of the mask must be aligned, that is, the substrate and reticle must be aligned. The substrate on which the first layer of patterns has been transferred by exposure is formed with a plurality of shot areas (chip patterns) provided with positioning marks called alignment marks. These shot areas are regularly arranged based on array coordinates set in advance on the substrate.
However, even if stepping a substrate based on the designed array coordinate values of a plurality of shot areas (shot array) on a substrate, the substrate will not always be accurately positioned due to the four factors (six error parameters) of the (a) residual rotational error Θ of the substrate, (b) orthogonality error Ω of the stage coordinate system (or shot array), (c) scalings Γ x, Γy of the substrate, (d) offsets (parallel movements) Ox, Oy of the substrate (center position).
Therefore, in the past, an enhanced global alignment (EGA) system has been used which statistically processed the measurement values obtained from a plurality of shot areas (sample shots) selected from a substrate to find the array of all of the shot areas on the substrate and positioned the shot areas in accordance with this array.
An EGA system uses the least square method to determine a conversion matrix to minimize the average error between array coordinate values obtained by actual measurement of sample shots and calculated array coordinate values obtained by entering designed array coordinate values of the shot areas into a predetermined model equation, calculates the calculated array coordinate values of positions for actual positioning based on this determined conversion matrix and the designed array coordinate values, and positions the shot areas of the substrate based on the calculated coordinate values.
Further, in addition to array error of shot areas on a substrate, shot areas suffer from overlay error in the shot areas due to the three factors of (a) residual rotational error θ of the shot area, (b) orthogonality error ω in the shot area, and (c) scalings γx, γy of the shot area.
Therefore, an EGA system is also known which uses a conversion matrix using a total of 10 error parameters including these three amounts of error (four error parameters) so as to find the array coordinate values for each shot area and the amounts of correction for overlay error for each shot area.
When employing this type of EGA system for alignment, which sample shots (number and positions) are measured or which measuring device is used when there are a plurality of types of measuring devices (detectors) has a great effect on the computation results, so these are preferably optimized. As such optimization technology, as disclosed in Japanese Patent No. 3313543, it is known to successively change the positions of the marks to be measured (sample shots) and the detector for EGA computation and select the combination of the mark positions and detector giving the smallest residual error component (random component) according to the plurality of EGA computation results as the optimal alignment parameters.
However, optimalization of such alignment parameters is designed to enable circuit patterns actually transferred by exposure to a substrate to be overlaid over previously formed circuit patterns with a high precision.
However, in the conventional art for optimization of the alignment parameters, the alignment parameters giving the smallest residual error component from the design values in the processing are selected as the optimal alignment parameters, so the overlay of the circuit patterns actually transferred by exposure on the substrate is not necessarily optimized. Even if the residual error component in the computation is the smallest, sometimes the overlay of circuit patterns is actually not sufficient. Even if the residual error component is not the smallest, there is a possibility of alignment parameters with higher precision of overlay of the circuit patterns.
Here, regarding the combination of the various types of alignment parameters, it may be considered to actually transfer by exposure and develop circuit patterns on a substrate, then measure the results of overlay of the circuit patterns (overlay error) and determine the best alignment parameters of the overlay results as the optimal alignment parameters. However, there are a huge number of combinations of alignment parameters. Measuring the overlay for all of these would require tremendous time and cost etc., so employing this technique is de facto difficult.